Put a secondary IP address and netmask on the interface; then change the desktops and servers one at a time (if manually assigned) or put a new DHCP server on the VLAN with addresses in the new range (after disabling the existing DHCP scope for the old IP subnet).
Depending on your situation, you can take your time (if you have Layer 3 switching) or you should hurry up (if routing between old and new subnet IPs goes through the same LAN interface on a router).
When "show ip arp" gives you no more IP addresses on the old subnet (other than the Cisco device's directly-connected LAN interface), copy and paste a sequence of commands from the console port to make the secondary IP address the primary IP address, and vice versa. After an appropriate amount of time, delete the secondary (old) IP address. Done.
There are tricks you can pull, for example shortening the lease period on DHCP addresses that are handed out, to get them checking for new IP addresses more frequently before you begin the address migration process. Whether you use them depends on how many stations you have to cut over, how many people you have helping, and how much time you have. But the above approach should be sufficient to get you where you want to be.
Oh yea, don't forget that most IP printing has the printers defined by their IP addresses. So if/when you change the IP address of a printer, you will have to also change the printer port definition on any and all machines that were printing directly to that printer's IP address. (If you're printing to print queues on a server, it's a little easier.)
And also, if you have HOSTS, LMHOSTS, DNS, or WINS/NBNS servers, you may have to update these name-to-IP-address resolution resources too.
Furthermore, if you have access control lists on routers, L3 switches, firewalls, or proxy servers, in order to restrict or allow specific traffic flows, you will need to update these as well to account for the new IP subnet(s).
Address changes are a PITA. No matter how well you plan to make it smooth, it always seems like something will bite you. Do your best to prepare for it in advance, though, and it won't hurt all that much. Make sure the most important things get cut over first and are working; sometimes people can wait to print, etc. And always have a retreat plan ready before you go charging in.
Maybe someone here can post the relevant RFC, I think there is one for going through the readdressing process.
Hope this helps.
UPDATE: Look for RFC's 1900, 1916, 2071, and 2072, plus search the Internet for "renumbering" or "PIER", the "Procedures for Internet/Enterprise Renumbering (PIER) working group in the IETF."
